As shown before, for least square regression the primal distributed ADMM uses \(_{p}\)  for linear updating. Since we directly obtain the linear convergence, we define the convergence rate of primal distributed ADMM as the spectral radius of linear mapping matrix \(_{p}\) , \(\rho (_{p})\) . From previous literature, primal distributed ADMM converges for any constant step size and \(\rho (_{p})<1\)  ([1]}). The data structure that leads to worst convergence rate depends on the choice of step size \(\rho _{p}\) . In the following theorem, we provides the results when step size is relatively large.
